3.The following rates are actual yields in % on US yield curve observed on the dates given:

Date	1 Mo	2 Mo	3 Mo	6 Mo	1 Yr	2 Yr	3 Yr	5 Yr	7 Yr	10 Yr	20 Yr	30 Yr
3/9/2019	2.06	2.01	1.98	1.88	1.72	1.47	1.38	1.35	1.42	1.47	1.77	1.95
16/2/2022	0.03	0.17	0.38	0.67	1.09	1.52	1.75	1.90	2.00	2.03	2.39	2.34

a) Plot the yield curves for 3 September 2019 and 16 February 2022. Interpret these yield curves on investor expectations with regards to the future state of the US economy.

b) Given information about yields on 16/2/2022, i) calculate the expected 3-year yield that the market is expecting between 16 February 2022 and 16 February 2025. ii) calculate the 20-year yield that is expected to prevail between 16 February 2032 and 16 February 2052 under the expectations theory of the term structure of interest rates.